Question: Express this quotient in scientific notation: ${\frac{3.800\times 10^{9}} {4.0\times 10^{2}}}$
Explanation: Start by collecting like terms together. $= {\frac{3.800} {4.0}} \times{\frac{10^{9}} {10^{2}}}$ Then divide each term separately. When dividing exponents with the same base, subtract their powers. $= 0.95 \times 10^{9\,-\,2}$ $= 0.95 \times 10^{7}$ To write the answer correctly in scientific notation, the first number needs to be between $1$ and $10$ . In this case, we need to move the decimal one position to the right without changing the value of our answer. $ $ We can use the fact that $0.95$ is the same as $9.50 \div 10$ , or $9.50 \times 10^{-1}$ $ = {9.50 \times 10^{-1}} \times 10^{7} $ $= 9.50\times 10^{6}$